Homeland Security Secretary Janet Napolitano has this pearl of advice for lawmakers eyeing immigration reform: The measure of border security cannot be reduced to a number.

A quantitative measure of a safe and secure border, however, is what some lawmakers on Capitol Hill have been asking for, to provide proof to Americans that Congress has plugged the nation's borders and won't risk the buildup of millions more illegal immigrants a decade from now.

Moreover, negotiators working to hammer out bipartisan legislation on immigration reform are expected to make any change in the status of illegal immigrants – of which there are at least 10 million – contingent upon improvements in border security. So, unless Congress or the Department of Homeland Security (DHS) comes up with a way to measure progress toward securing the border, the fate of the undocumented could twist in the wind, satisfying neither those who are concerned about border security nor those who want to bring people out of the shadows. This sticking point of how to measure border security could unravel the entire reform bill.

But Secretary Napolitano, a former governor of the border state of Arizona, told reporters at a breakfast sponsored by The Christian Science Monitor on Tuesday that DHS will not produce a comprehensive border security measurement – and not for lack of trying.

Several years ago, DHS put forward the idea of a “Border Condition Index,” which would blend traditional border security metrics such as number of apprehensions of illegal border-crossers or number of drug confiscations with broader measures like crime rates and property values in border areas.

“It turns out,” Napolitano said, “that is a very difficult thing to do in any kind of statistically significant way.”

She went on to explain that her department approaches measuring border security in terms of responsiveness to known threats. She said the record number of border agents and improved aerial surveillance, among other things, have made identifying and blocking illegal border crossings more effective than ever – and thus that the border is secure, by and large.

“What you want is the ability to spot illegal traffic, particularly in the highly trafficked areas,” she said, “and then the ability to respond to what is seen. Using that measure, we are confident that the border is as secure as it’s ever been.”

On Capitol Hill, lawmakers recognize that coming up with a catch-all number to rate border security is neither easy nor, perhaps, even possible. Members of both parties represent areas along the 2,000-mile border with Mexico and understand that "security" out in the Arizona desert means something different than it does near urban San Diego.

Still, lawmakers are frustrated that DHS isn’t making headway on new metrics and, in recent congressional testimony, ruled out use of the department's Border Condition Index as a metric in their immigration reform legislation.

This frustration bubbled up at a recent congressional hearing, where lawmakers heard from the acting commissioner of the Customs and Border Patrol, whose comments about the challenges of distilling border security into a single number were similar to Napolitano’s. Said Rep. Candice Miller (R) of Michigan, chairman of the Homeland Security subcommittee devoted to border and maritime security: “I am certainly open to a series of measures that could better inform the security in the vastly different terrain along the border or at our ports of entry and in the maritime environment.... Unfortunately, such measures do not exist today. They don't seem to be ready in the near term.”

That’s a problem for immigration reform, Representative Miller said.

“We have to be able to have a robust way of measuring [border security], something that can be explained – easily explained – to the American people that we're going in the right direction,” she said.

Several proposals have addressed this shortcoming. Most recently, Sen. Rand Paul (R) of Kentucky suggested that Congress should vote every year for five years on whether the border is secure, in order to certify sufficient progress.

The Senate’s bipartisan group of eight senators negotiating immigration reform, on the other hand, envision a new commission – made up of Southwest border leaders including governors, attorneys general, and community advocates – that would determine when the border security reforms that the group seeks have been sufficiently attained.

What none of these groups proposes?

A number.

“There’s no one number [that] catches” the issue of border security, Napolitano said Tuesday. “That is the problem: If you’re looking at border security, you’re looking at a lot of different things.”